Journal of the Mathematical Society of Japan

Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials

Yoshihiro MIZUTA, Eiichi NAKAI, Takao OHNO, and Tetsu SHIMOMURA

Full-text: Open access

Abstract

Our aim in this paper is to deal with boundedness of fractional integral operators on Morrey spaces L(1,φ)(G) and the Sobolev embeddings for generalized Riesz potentials. Target spaces are Orlicz-Morrey, Orlicz-Campanato, and generalized Hölder spaces.

Article information

Source
J. Math. Soc. Japan, Volume 62, Number 3 (2010), 707-744.

Dates
First available in Project Euclid: 30 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1280496817

Digital Object Identifier
doi:10.2969/jmsj/06230707

Mathematical Reviews number (MathSciNet)
MR2648060

Zentralblatt MATH identifier
1200.26007

Subjects
Primary: 26A33: Fractional derivatives and integrals
Secondary: 31B15: Potentials and capacities, extremal length 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Keywords
Sobolev embeddings Morrey space Orlicz space Riesz potential fractional integral

Citation

MIZUTA, Yoshihiro; NAKAI, Eiichi; OHNO, Takao; SHIMOMURA, Tetsu. Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials. J. Math. Soc. Japan 62 (2010), no. 3, 707--744. doi:10.2969/jmsj/06230707. https://projecteuclid.org/euclid.jmsj/1280496817


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